Optimal scheduling of electric vehicles and photovoltaic systems in residential complexes under real-time pricing mechanism

Journal Pre-proof Optimal Scheduling of Electric Vehicles and Photovoltaic Systems in Residential Complexes under Real-Time Pricing Mechanism

Sahar Seyyedeh Barhagh, Mehdi Abapour, Behnam Mohammadi-Ivatloo PII:

S0959-6526(19)33911-3

DOI:

https://doi.org/10.1016/j.jclepro.2019.119041

Reference:

JCLP 119041

To appear in:

Journal of Cleaner Production

Received Date:

04 October 2018

Accepted Date:

24 October 2019

Please cite this article as: Sahar Seyyedeh Barhagh, Mehdi Abapour, Behnam Mohammadi-Ivatloo, Optimal Scheduling of Electric Vehicles and Photovoltaic Systems in Residential Complexes under Real-Time Pricing Mechanism, Journal of Cleaner Production (2019), https://doi.org/10.1016/j. jclepro.2019.119041

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Optimal Scheduling of Electric Vehicles and Photovoltaic Systems in Residential Complexes under Real-Time Pricing Mechanism Sahar Seyyedeh Barhagh*, Mehdi Abapour, and Behnam Mohammadi-Ivatloo Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran Tel./Fax: +98 41 33300829, P.O. Box: 51666-15813 [email protected], [email protected], [email protected] *Corresponding author

Abstract Residential complexes (RCs) consisting of photovoltaic (PV) systems, wind turbines and electric vehicles (EVs), have been rapidly extended in energy systems in recent years. Optimal scheduling of local generation units can lead to economic improvement in RCs. In this regard, optimization of the performance of RCs appears to be necessary. Operators of RC energy systems equipped with local generation units can benefit from demand response programs (DRPs) to reduce their operating costs while satisfying energy demands. Within these programs, energy consumers are motivated to change their consumption in a way that economic targets are satisfied. In this paper, optimal operation of a grid-connected EV/PV RC energy system is studied under real-time pricing of a DRP. The studied RC energy system is equipped with PV units and EVs that can support RCs in supplying energy demands and providing economic benefits. The incorporated PV unit is modeled considering solar irradiance parameters and ambient temperature, which can lead to accurate simulation results. Moreover, the proposed model for EVs can enhance the efficient operation of RCs through optimal charge and discharge processes. Further, the optimal operation of energy systems integrated into RCs is modeled as mixed-integer linear programming (MILP). Additionally, a general algebraic modeling system (GAMS) is used to carry out simulations in 1

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different scenarios and the results are presented for comparison. For the studied test case, the total expected cost of RCs is reduced by 37.31%, which represents the influential impact of demand response on the optimal scheduling of DG units. Keywords: Residential complex (RC), economic performance, photovoltaic (PV) system, electric vehicle (EV), real-time pricing (RTP) of demand response program (DRP). Nomenclature Indices t

s Variables cost I d ,s I dif , s I g ,s load , NC pDRP ,t , s

,C ptload ,s

Time period index Scenario index Total operation cost of RC Direct normal irradiance Diffuse horizontal irradiance Global horizontal irradiance Non-critical load under RTP Critical load

, Nc ptload ,s

Non-critical load

Pt imp ,s

Imported power from the upstream grid Exported power to the upstream grid Charge power of EV Discharge power of EV Output power of PV systems

exp t ,s

P

Pt chev ,s Pt ,dchev s

Pt ,pvs SOCt , s Arive t ,s

SOC

SOCtDep ,s

Tt ,as Tt c, s

State of charge of EV State of charge of EV at arrival time per scenario State of charge of EV at departure time Ambient temperature Temperature of cells

Binary Variables Btch, s Btdch ,s I timp ,s I texp ,s

A binary variable of EV’s charging condition A binary variable of EV’s discharging condition A binary variable for power import A binary variable for power export

Parameters 2

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tchev tdchev timp texp 



 s



E

Mt nsPV

n pPV NOCT imp min

P

imp Pmax exp Pmax exp Pmin chev Pmax dchev Pmax

PstcPV mppt Pt ,max

RTt price

SOCmin SOCmax Arive SOCMax

SOC

Dep desired

SN

T

Rate of charge of EV Rate of discharge of EV Price of imported electric power from the upstream grid Price of exported electric power to the upstream grid The incidence angle of solar radiation on a tilted surface A tilted angle Surrounding reflection Scenario probability Temperature coefficient of PV systems Demand-price elasticity coefficient Availability of EV PV panel numbers in series PV panel numbers in parallel Nominal temperature of the operating cell Minimum imported power from the upstream grid Maximum imported power from the upstream grid Minimum exported power to the upstream grid Maximum exported power to the upstream grid Maximum charge power of EV Maximum discharge power of EV The PV output at the maximum power point and the standard test condition Maximum power of the PV converter Real-time power price Minimum state of charge of EV Maximum state of charge of EV Maximum state of charge of EV at arrival time Desired state of charge of EV at departure time Scenario number Scheduling horizon

1. Introduction Nowadays, due to the crises induced by fossil fuel over-consumption, renewable energy sources such as wind turbines (Fathabadi, 2017; Mirzaei et al., 2019; Shezan et al., 2016) and photovoltaic (PV) systems (Bukar and Tan, 2019; Majidi et al., 2017; Shezan et al., 2016) have been extensively

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used in power systems. These sources generate clean and inexpensive energy to satisfy energy demands. However, the intermittent generation of these sources can cause many problems for operators of energy systems. In order to handle these issues, electric vehicles (EVs) (Aliasghari et al., 2018; Fathabadi, 2018a; Li et al., 2018; Lu et al., 2018; Sedighizadeh et al., 2018) can be integrated with other energy sources in power systems. In this section, a summary of studies about the operation of residential microgrid energy systems under incorporation of distributed generation (DG) units in various fields is presented. Renewable sources have been among the most suitable options for energy sources in microgrids. Different types of these sources have been integrated into microgrids to satisfy different objectives. For instance, the energy management problem was studied in microgrids consisting of solar and wind units, boilers, micro-turbines, CHP and energy storage systems under different loads (Tabar et al., 2017). Moreover, a residential microgrid containing a mini-size wind turbine and PV panels was managed using a novel strategy to improve the grid power profile and reduce power peaks (Pascual et al., 2015). In another investigation (Sreedharan et al., 2016), different strategies were used to minimize the monthly energy bill of the University of California-San Diego by integrating renewable energy sources. Implementing the genetic algorithm, unit commitment problem and the economic dispatch problem of renewable units in microgrids were evaluated (Nemati et al., 2018). Moreover, the optimum energy management of microgrids was studied to reduce the total cost of buying power from different sources like as PV units, wind turbines, hydro-electric units, thermal units and gas-fired power generation systems (Abedini et al., 2016). In another work (Numbi and Malinga, 2017), the cost-effective performance of a PV-based residential microgrid energy system was examined under feed-in tariff, in which the payback index was employed to assess the economic operation of the studied system.

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Renewable-based microgrids can be stable enough to supply energy consumers in islanded/isolated operation modes. In ref (Rokni et al., 2018), a distributed energy management methodology was implemented based-on alternating direction method of multipliers to optimize the performance of grid-connected/islanded PV-based microgrids under power flow limitations. In order to control the operation of an isolated microgrid that includes renewable energy sources, a robust technique was provided to avoid frequency instabilities in probable contingencies (Kerdphol et al., 2018). Microgrids may include different types of distributed energy sources (DERs) including renewable and non-renewable. In order to share power among coupled DERs in an autonomous islanded microgrid under unbalanced loads, a robust control methodology was employed (Gholami et al., 2018). Moreover, the optimal design of hybrid electric power generation systems including renewable units such as PVs were obtained for isolated zones using meta-heuristic optimization techniques such as particle swarm optimization (Galindo Noguera et al., 2018). Integrating renewable sources can result in hybrid energy systems for various applications in power systems, especially in microgrids. The optimal planning and design of hybrid renewable energy systems for microgrid applications was obtained using the distributed energy resources customer adoption model in (Jung and Villaran, 2017). Authors in ref (Fathabadi, 2018b), presented a novel model to replace internal combustion engine of vehicles with renewable units such as wind turbines and PV systems. Moreover, in (Zehir et al., 2017), the operation analysis of secondary distribution networks comprising renewable-based microgrids was focused on to solve distribution network related problems such as voltage instabilities, power losses, etc. Optimal sizing and siting of renewable units in microgrids were also considered in some researches. In the research presented in (Pesaran H.A et al., 2017), optimum placement problems of DG units including renewable sources were reviewed in terms of different parameters such as

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type of problem, utilized methods, etc. In ref (Hong et al., 2017), renewable energy generation sources were optimally sized in a community microgrid using a novel method based on the Markov model and by incorporating the interior-point algorithm. Demand side management programs were implemented in research papers to improve the performance of microgrids. By implementing two demand response programs (DRPs) based on time-of-use and real-time pricing (RTP) in (Nikmehr et al., 2017), the optimal day-ahead scheduling of microgrids consisting of different types of renewable energy sources was studied to minimize total operation cost with the use of particle swarm optimization (PSO). In (Aghajani et al., 2017), demand response packages were proposed as options for controlling renewable uncertainties. Moreover the multi-follower bi-level programming was used to minimize the energy cost of the distribution network operator under the assumption of multi-microgrids and DRPs (Jalali et al., 2017). Furthermore, a multi-objective energy management system was provided, in which the microgrid performance was optimized in the presence of uncertainty of renewable units and demand response providers (Aghajani et al., 2015). Demand response providers cover the uncertainties of wind units and PV systems. In this regard, the optimum component size of microgrids was obtained using a DRP to balance the generation and consumption of energy and peak load and minimize their cost (Amrollahi and Bathaee, 2017). Similar problems have also been studied along with EV scheduling (Zifa Liu et al., 2018; SoltaniNejad Farsangi et al., 2018). As one of the novel technologies being rapidly expanded in energy systems, especially in microgrids, EVs have been incorporated to improve the operation of microgrids by providing various services. The impact of integrating different types of EVs with various characteristics and renewable units into the power systems was investigated (Fathabadi, 2015). In order to handle the optimal operation of microgrids in the presence of plug-in hybrid electric vehicles (PHEVs), robust

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optimization was employed to minimize the operation cost of microgrids while taking possible risks into account (Bahramara and Golpîra, 2018). In (Kamankesh et al., 2016), the implementation of a new robust and symbiotic organism search (SOS) algorithm for optimal energy management of microgrids containing PHEVs, storage devices and renewable energy sources was evaluated, in which the overall system covering cost of local generation units as well as cost of interaction between the upstream network and the microgrid was minimized. By implementing a new optimization algorithm based on the bat algorithm, optimal scheduling of electric power units was studied in renewable-based local distribution systems including PHEVs, in which the total network cost including cost of energy not supplied, reliability cost and cost of power supply for loads and PHEVs was minimized (Tabatabaee et al., 2017). By solving the non-linear optimization, an optimal day-ahead operation plan of microgrids was obtained to decrease the operation cost of microgrids under the optimum integration of EVs and by using the vehicle to grid (V2G) technology (Aluisio et al., 2017). Similarly, the V2G technology was employed to improve the operation of microgrids in unbalanced and isolated modes (Rodrigues et al., 2018), satisfy economic-environmental expectations and provide market opportunities with considering risks (Shamshirband et al., 2018). The placement and sizing of V2G technologies in a microgrid were studied in (Mortaz et al., 2019). Locations, in which energy systems such as charging stations are installed, play a key role in the operation of installed generation units. To analyze a location from different viewpoints, various factors should be taken into account and sufficient data from end-users should be collected, which can be achieved through innovative data collection technologies (Forati et al., 2015). In this regard, fast-charging stations were optimally located to maximize long-distance trip completion in the United States (He et al., 2019). It should be noted that with technology progress, wireless charging

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technologies have been innovated for EVs in recent years, which was summarized in (Machura and Li, 2019). With the aim of charging EVs by renewable energy sources and enhancing export capacity, the potential of smart charging of EVs was analyzed in (Pearre and Swan, 2016). In another investigation (Baccino et al., 2015), EVs were optimally scheduled in distribution networks, in which a novel optimization framework consisting of two stages was developed to take power flow constraints into account while optimizing the recharge power of EVs. To this end, first, power flow limitations were evaluated and, the optimum recharge power was obtianed for EVs. Penetration of EVs and control of their charge and discharge patterns in power systems could be challenged with different issues such as random arrival times. Optimum charge patterns were obtained for EVs through global and local scheduling schemes in ref (He et al., 2012). In doing so, a global scheduling scheme was developed to minimize the total cost considering the pre-known EV arrival. Moreover, a local scheduling scheme was developed to minimize the total cost in the current ongoing EV set in the local group. The results revealed that the local scheduling scheme led to closer optimization results. Similarly in ref (Sortomme and El-Sharkawi, 2012), a unidirectional vehicle to grid technology was employed to provide energy and ancillary services to an electricity network. According to the model proposed in their study, consumers and utilities can have the most optimal performance by benefiting from the provided options. In another research (Wu et al., 2019), a data-driven non-parametric joint chance-constrained optimization model was developed for the optimal economic dispatch of PV-based energy system, in which the uncertainty of power generated by a PV system was taken into account through the proposed model.

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In this paper, a mathematical-based optimization framework is presented for energy management of a residential complex (RC) in South Africa, which includes a specific energy consumption pattern. The mentioned RC is a grid-connected energy system, in which renewable generation units such as PV systems as well as storage technologies such as EVs are integrated in order to enhance its performance from various viewpoints. PV systems can generate clean and inexpensive power to be used for either load supply or export process. The accurate modeling of PV generation is necessary to have real particle simulation results. Thus, a precise mathematical-based model is proposed to formulate the output power of PV systems. EVs can manage energy consumption within RC by handling the intermittent generation of PV systems through optimal charge and discharge processes. In fact, EVs can have bidirectional power exchange (charge/discharge) with the RC, and charge/discharge processes can help the RC optimize the energy consumption and control the intermittent generation of PV systems. The discharged power by EVs can be used to supply demand in peak-time periods, which can mitigate the negative economic impact of power imported from the upstream network in the mentioned periods. Similar to PV systems, a mathematical-based model is proposed to model the operation of EVs. In order to assess the performance of the RC toward DRPs, an RTP mechanism is proposed and the RC performance is evaluated from different economic viewpoints. It is worth mentioning that in order to optimize the energy system operation, different valuable methodologies have been previously introduced, one of which has been the chance constraint optimization method. This method is mostly used to solve optimization problems with considering probabilistic conditions (Zhaoxi Liu et al., 2018). At first, different scenarios with various probabilities are generated for uncertain parameters and, then according to this method, the probability of satisfying a specific constraint is ensured (Odetayo et al., 2018). The main focus of the proposed mathematical-based model is to optimally integrate

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renewable energy sources such as PV units as well as storage facilities such as EVs into RC systems that might include energy demands with different patterns. Moreover, the proposed model seeks to assess the impact of DRPs such as RTP on the economic performance of RCs in countries like South Africa. Therefore, contributions of the conducted study can be expressed as follows: 

The optimal operation of a renewable-based RC considering the real data of the city of Durba in South Africa;



The utilization of EVs to handle the intermittent generation of PV systems and gain economic benefit;



The implementation of RTP to improve the RC performance by reducing total operation cost;



The proposal of a comprehensive optimization framework based on MILP for optimal energy management and uncertainty management in a grid-connected RC with local energy units.

Other parts of the conducted paper are classified as follows: Mathematical formulations are presented in Section 2. Simulations and corresponding results are presented in Section 3. Finally, conclusions are presented in Section 4. 2. Problem formulation The proposed optimization model is mathematically formulated in this section for the economic performance of a grid-connected RC containing PV system and EV with RTP. 2.1. Objective function As the objective function, the total cost of the RC including the cost of power imported from the RC minus the revenue obtained from power exported to the upstream grid should be minimized as in Eq.1.

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T  SN imp exp  Min obj  cost     s    Pt imp - Pt ,exp    TP , s  t s  t t  s 

(1)

where obj is the objective function, cost is the total operation cost of RC, SN is the number of scenarios, s is the scenario index, T is the scheduling horizon, t is the time period, Pt imp is the ,s imported power from the upstream grid, timp is the price of power imported from the upstream grid, Pt exp is power exported to the upstream grid, texp is the price of power exported to the ,s upstream grid and TP is the number of scheduling days. 2.2. Energy balance constraint The required power for critical and non-critical loads is received from the output power of the PV system, the upstream grid and the discharge power of the EV. The mentioned explanations are mathematically modeled in Eq.2. (2)

,C , Nc exp dchev ptload  ptload  Pt ,pvs  Pt imp  Pt chev ,s ,s , s  Pt , s  Pt , s ,s

where EV,

,C load , Nc ptload is the critical load, pt , s is the non-critical load, ,s

Pt ,pvs is the output power of the PV system and

is the charge power of the Pt chev ,s

is the discharge power of the EV. Pt ,dchev s

2.3. Distributed generation (DG) unit limitations In this section, the limitations of DG units and the EV are presented through Eqs.3-13. 2.3.1. Photovoltaic (PV) system Renewable units such as PV systems can play positive roles in the optimal operation of energy systems. Power generated by these systems is usually intermittent. Therefore, accurate modeling of these units is necessary for accurate simulation results. The proposed model for the PV system in this paper is a comprehensive mathematical-based model taken from (Numbi and Malinga, 2017), according to which the output of the PV system is proportional to solar irradiance, cell 11

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temperature, number of PV panels in series and parallel and other relevant factors. The proposed model is expressed in Eqs.3-5 (Numbi and Malinga, 2017).

Pt ,pvs  PstcPV  nsePV  n paPV  I d , s  cos    I dif , s 

1- cos   (1  cos  )    I g ,s   (1-   (Tt c, s - 25)) 2 1000

(3)

where PstcPV is the PV output at the maximum power point and the standard test condition, nsePV is the number of PV panels in series,

PV n pa is the number of PV panels in parallel,

I d , s is the direct

normal irradiance,   is the incidence angle of solar radiation on a tilted surface, I dif , s is the diffuse horizontal irradiance,  is the tilted angle,  is the surrounding reflection, I g , s is the global horizontal irradiance,  is the temperature coefficient of the PV system and

Tt c, s is the temperature

of cells. The temperature of cells mentioned above is proportional to the ambient temperature, which is expressed in Eq.4.

Tt c, s  Tt ,as  I d , s  cos    I dif , s  where

1- cos   (1  cos  )    I g ,s   ( NOCT - 20) 2 2  800

Tt ,as is the ambient temperature and

(4)

NOCT is the nominal temperature of the operating cell.

The output power of the PV system should be within the legal nominal range as follows: mppt Pt ,pvs  Pt ,max

(5)

mppt where Pt ,max is the maximum power of the converter.

2.3.2. Electric vehicle model The integrated EV is modeled through Eqs.6-13 (Jannati and Nazarpour, 2017). EVs can optimally charge and discharge power to optimize energy consumption in RCs. However, there are some limitations such as availability of EVs, charge and discharge rates and others that should be taken 12

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into account in modeling such energy units. The total charge power of the EV with regard to its availability should be less than the rated charge value, which is expressed in Eq.6. Moreover, the discharge power of the EV within the available period is limited to be less than the nominal discharge rate, which is expressed in Eq.7. Finally, when the EV is available, charge and discharge processes should not occur at the same time, which is expressed in Eq.8. (6)

chev Pt chev  Pmax  Btch, s  M t ,s

chev where Pt chev is the charging power of the EV, Pmax is the maximum charge power of the EV, Btch, s ,s

is the binary variable of the EV charging condition and M t is the availability of the EV. (7)

dchev Pt ,dchev  Pmax  Btdch s ,s  M t

dchev where Pt ,dchev is the discharge power of the EV, Pmax is the maximum discharge power of the EV s

and Btdch is the binary variable of the EV discharging condition. ,s (8)

Btch, s  Btdch ,s  M t

The state of charge (SOC) of the EV at present hour depends on SOC in previous hour and charge and discharge processes. The SOC of the EV is mathematically expressed in Eq.9. SOCt , s  SOCt -1, s  Pt chev tchev ,s

Pt ,dchev s

(9)

tdchev

where SOCt , s is the SOC of the EV, tchev is the rate of charge of the EV and tdchev is the rate of discharge of the EV. The SOC of the EV is limited by Eq.10. (10)

SOCmin  SOCt , s  SOCmax

where SOCmin and SOCmax are the minimum and maximum SOC of the EV, respectively.

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The limitations related to the SOC of the EV at arrival and departure time are expressed in Eqs.1113. It is worth mentioning that in order to consider different driving patterns, the scenario-based methodology is utilized to generate scenarios in order to model the stochastic nature of the SOC value at the arrival time of the EV. (11)

Arive SOCtArive  SOCMax ,s

Arive where SOCtArive is the SOC of the EV at arrival time and SOCMax is the maximum SOC of the EV ,s

at arrival time. Dep SOCtDep , s  SOCdesired

(12)

Dep SOCdesired  SOCmax

(13)

Dep where SOCtDep is the SOC of the EV at departure time and SOCdesired is the desired SOC of the ,s

EV at departure time. 2.3.3. Upstream grid Power exported from the RC grid to the upstream grid and power imported from the upstream grid to the RC grid are limited by Eqs.14-15. According to Eq.14, total exported power cannot exceed the nominal power of the line connecting the RC to the upstream grid. Moreover, as expressed in Eq.15, total imported power should be within the nominal limitation of the mentioned line. Finally, Eq.16 is used to limit the simultaneous import and export of power. Specifically, when power is exported, the binary variable I texp is equal to 1. Similarly, when power is imported, the binary ,s variable I timp is equal to 1. Therefore, according to Eq.16, import and export processes cannot ,s occur simultaneously. (14)

exp exp exp exp I texp , s  Pmin  Pt , s  I t , s  Pmax

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exp exp where I texp is the binary variable for power export and, Pmax and Pmin are, respectively, the ,s

maximum and minimum power exported to the upstream grid. imp imp imp I timp  I timp , s  Pmin  Pt , s , s  Pmax

(15) imp imp where I timp is the binary variable for power import and, Pmin and Pmax are, respectively, the ,s

maximum and minimum power imported from the upstream grid. (16)

imp I texp ,s  It ,s  1

2.3.4. Real-time pricing (RTP) mechanism In some hours within a day, due to peak power consumption, the price of electricity increases and, therefore, total energy consumption cost within the mentioned periods increases proportionally. One option to handle energy consumption in such periods is DRPs. DRPs can help consumers manage their consumption efficiently to reduce their payments. In this paper, the RTP of DRP is used, which enables consumers to revise their consumption pattern according to the rates of energy determined previously. RTP is formulated in Eq.17 (Numbi and Malinga, 2017). load , NC load , Nc , Nc pDRP  E  ptload  , t , s  pt , s ,s



imp t

- RTt price 

(17)

RTt price

load , NC where pDRP , t , s is the non-critical load under RTP, E is the demand-price elasticity coefficient ([-

0.5, 0]) and RTt price is the real-time power price. 3. Numerical study In this section, the optimal operation of the PV-based RC under the implementation of the EV is numerically studied without and with RTP. The studied RC is captured in Fig. 1. The proposed problem is modeled as an MILP and the GAMS software is employed to solve it (Soroudi, 2017).

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Fig. 1. Studied PV-EV-based RC

3.1. Input data Input data necessary for conducting simulations are presented below: Critical and non-critical load profiles, real-time and upstream grid prices, sunlight irradiations and ambient temperature around the PV system, technical data of the PV system and technical parameters of the upstream grid are taken from (Numbi and Malinga, 2017). Furthermore, the technical data related to the EV and availability of the EV for charge and discharge processes are taken from previous studies (Jannati and Nazarpour, 2017). The probability of each scenario and the value of uncertain parameters in each scenario are presented in Tables 1-8. Table 1: The scenario’s probability

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Scenario 1 2 3 4 5 6 7 8 9 10

Probability 0.04 0.06 0.02 0.09 0.05 0.06 0.07 0.09 0.08 0.05

Scenario 11 12 13 14 15 16 17 18 19 20

Probability 0.04 0.05 0.07 0.03 0.04 0.05 0.06 0.01 0.03 0.01

Table 2: The SOC value at the arrival time of the EV SOCtArive SOCtArive (kWh) (kWh) Scenario Scenario ,s ,s 1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

0.5397 0.7134 0.7031 0.5978 0.6506 0.5357 0.5882 0.6826 0.6488 0.7047

Table 3: The critical load value per scenario ,C ptload (kW) ,s

Time 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

0.6537 0.6789 0.5316 0.6817 0.6203 0.5223 0.5648 0.6071 0.7033 0.7086

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

0.0 0.2

0.0 0.3

0.0 0.3

0.0 0.3

0.0 0.3

0.0 0.2

0.0 0.2

0.0 0.3

0.0 0.2

0.0 0.3

0.0 0.3

0.0 0.3

0.0 0.3

0.0 0.3

0.0 0.3

0.0 0.2

0.0 0.2

0.0 0.3

0.0 0.3

0.0 0.2

0.3 0.2 0.0 0.2 0.3 0.2 0.0 0.3 0.3 0.3 0.0 0.2 0.5 0.5 0.3 0.6 1.9 1.6 2.1 2.0 2.0

0.2 0.3 0.0 0.2 0.3 0.3 0.0 0.3 0.3 0.3 0.0 0.2 0.5 0.4 0.3 0.5 1.8 1.8 1.9 1.9 1.8

0.3 0.2 0.0 0.2 0.3 0.3 0.0 0.2 0.3 0.3 0.0 0.2 0.5 0.5 0.2 0.5 1.9 1.9 1.8 2.0 1.6

0.3 0.2 0.0 0.3 0.3 0.3 0.0 0.3 0.2 0.3 0.0 0.2 0.6 0.5 0.2 0.5 1.6 1.8 2.0 2.0 1.8

0.2 0.3 0.0 0.3 0.3 0.2 0.0 0.2 0.3 0.2 0.0 0.2 0.5 0.5 0.3 0.5 1.7 1.3 1.6 1.7 1.8

0.2 0.2 0.0 0.2 0.2 0.2 0.0 0.2 0.2 0.2 0.0 0.2 0.4 0.5 0.3 0.6 1.7 1.7 1.5 2.2 2.1

0.2 0.3 0.0 0.2 0.3 0.3 0.0 0.3 0.3 0.2 0.0 0.3 0.6 0.5 0.2 0.6 1.5 1.6 1.6 1.7 1.9

0.2 0.2 0.0 0.3 0.3 0.3 0.0 0.3 0.2 0.2 0.0 0.2 0.5 0.4 0.3 0.6 1.6 1.6 1.6 2.0 1.9

0.2 0.3 0.0 0.3 0.2 0.2 0.0 0.3 0.2 0.3 0.0 0.3 0.5 0.4 0.3 0.5 1.6 1.5 1.7 2.2 1.9

0.3 0.2 0.0 0.3 0.3 0.2 0.0 0.3 0.3 0.3 0.0 0.2 0.5 0.5 0.3 0.5 1.8 1.8 1.7 1.9 1.7

0.2 0.3 0.0 0.3 0.2 0.3 0.0 0.2 0.3 0.2 0.0 0.2 0.6 0.5 0.2 0.5 1.6 1.6 1.4 2.1 1.8

0.3 0.3 0.0 0.3 0.3 0.2 0.0 0.3 0.2 0.3 0.0 0.2 0.5 0.6 0.3 0.5 1.9 1.5 1.8 2.2 1.8

0.3 0.3 0.0 0.2 0.2 0.3 0.0 0.2 0.3 0.2 0.0 0.3 0.5 0.6 0.3 0.6 1.8 1.6 1.6 2.2 1.6

0.3 0.3 0.0 0.3 0.2 0.2 0.0 0.3 0.3 0.3 0.0 0.3 0.5 0.5 0.3 0.6 1.6 1.6 1.6 2.3 1.8

0.2 0.2 0.0 0.2 0.2 0.2 0.0 0.3 0.3 0.2 0.0 0.3 0.5 0.5 0.3 0.5 1.7 1.7 1.9 1.8 1.9

0.3 0.3 0.0 0.2 0.2 0.3 0.0 0.3 0.2 0.3 0.0 0.3 0.5 0.6 0.2 0.5 1.7 1.7 2.0 1.9 1.8

0.2 0.3 0.0 0.3 0.2 0.3 0.0 0.2 0.2 0.2 0.0 0.3 0.5 0.5 0.3 0.4 1.8 1.6 2.2 2.3 2.0

0.3 0.3 0.0 0.3 0.3 0.3 0.0 0.3 0.3 0.3 0.0 0.2 0.5 0.6 0.2 0.6 1.7 1.6 1.8 2.0 1.9

0.2 0.2 0.0 0.2 0.3 0.2 0.0 0.3 0.2 0.3 0.0 0.2 0.5 0.6 0.2 0.5 1.7 1.7 2.3 2.0 1.7

0.2 0.2 0.0 0.3 0.3 0.2 0.0 0.2 0.2 0.2 0.0 0.2 0.5 0.5 0.3 0.5 1.6 1.7 1.8 2.1 1.8

17

Journal Pre-proof

24

0.2

0.3

0.3

0.2

0.3

0.3

0.2

0.2

0.3

0.2

0.2

0.2

0.3

0.2

0.3

0.2

0.3

0.3

1

2

3

4

5

6

7

8

9

10

11

12

14

14

15

16

17

18

19

20

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0 2.0 1.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.1 2.0 0.5 0.4 0.0 0.0

0.0 1.9 1.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.9 2.1 0.5 0.4 0.0 0.0

0.0 2.2 1.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.0 2.2 0.4 0.4 0.0 0.0

0.0 2.4 2.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.4 2.1 0.5 0.4 0.0 0.0

0.0 1.6 2.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.8 1.6 0.4 0.4 0.0 0.0

0.0 2.0 1.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.8 2.1 0.4 0.5 0.0 0.0

0.0 1.7 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.2 2.0 0.4 0.4 0.0 0.0

0.0 2.2 2.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.5 2.0 0.4 0.4 0.0 0.0

0.0 2.5 2.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.4 1.8 0.4 0.5 0.0 0.0

0.0 1.7 2.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.8 2.2 0.4 0.4 0.0 0.0

0.0 2.3 2.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.4 1.9 0.3 0.4 0.0 0.0

0.0 1.6 2.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.1 1.9 0.4 0.5 0.0 0.0

0.0 2.1 1.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.9 1.9 0.4 0.5 0.0 0.0

0.0 2.2 2.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.5 1.9 0.4 0.5 0.0 0.0

0.0 2.0 1.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.6 2.0 0.4 0.4 0.0 0.0

0.0 2.2 1.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.8 2.0 0.5 0.4 0.0 0.0

0.0 2.3 2.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.9 1.9 0.5 0.5 0.0 0.0

0.0 2.1 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.7 1.9 0.4 0.4 0.0 0.0

0.0 1.8 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.7 2.0 0.5 0.4 0.0 0.0

0.0 1.8 2.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.4 2.1 0.4 0.4 0.0 0.0

Table 5: Direct normal irradiance per scenario I d , s (w/m2)

Time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0.3

Table 4: The non-critical load value per scenario , Nc ptload (kW) ,s

Time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0.3

1

2

3

4

5

6

7

8

9

10

11

12

14

14

15

16

17

18

19

20

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

376

342

362

426

478

398

404

503

480

433

508

444

396

431

385

392

433

417

405

425

644

616

611

616

605

520

639

764

581

718

580

676

597

590

556

534

573

640

651

634

595

854

886

833

642

752

818

823

717

728

811

772

800

720

704

850

832

893

680

706

736

843

772

951

736

701

857

908

803

767

810

777

847

956

873

737

821

710

845

830

1160

985

902

1018

806

880

1037

1031

956

932

869

1043

801

961

939

993

882

966

993

864

943

1121

943

890

959

898

996

911

929

978

1110

890

1023

991

1088

759

897

970

877

862

983

961

952

970

776

895

920

866

984

1030

877

988

830

1022

830

952

899

1012

932

929

1039

896

919

1098

770

1110

849

971

951

973

898

960

1013

738

803

1113

967

863

908

823

857

854

874

820

878

807

1023

794

1049

890

761

877

971

989

924

958

1028

768

867

760

709

821

822

866

792

662

886

841

732

784

944

820

853

763

770

788

728

828

777

805

606

569

634

616

689

687

666

567

509

648

605

737

770

602

692

718

654

714

739

646

604

580

458

561

590

572

550

656

623

628

551

582

634

654

594

522

592

486

556

594

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

18

Journal Pre-proof

21 22 23 24

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Table 6: Diffuse horizontal irradiance per scenario I dif , s (w/m2)

Time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

1

2

3

4

5

6

7

8

9

10

11

12

14

14

15

16

17

18

19

20

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0 0 125 331 132 120 177 140 146 154 130 142 149 148 0 0 0 0 0 0 0

0 0 0 114 317 190 138 150 166 142 133 129 164 140 142 0 0 0 0 0 0 0

0 0 0 121 314 197 126 138 140 141 136 132 164 156 112 0 0 0 0 0 0 0

0 0 0 142 317 185 155 155 132 144 163 124 173 152 137 0 0 0 0 0 0 0

0 0 0 159 311 143 120 123 142 115 114 133 158 170 144 0 0 0 0 0 0 0

0 0 0 133 267 167 115 134 133 133 165 122 132 169 140 0 0 0 0 0 0 0

0 0 0 135 328 182 140 158 148 136 126 155 177 164 135 0 0 0 0 0 0 0

0 0 0 168 393 183 148 157 135 128 144 120 168 140 160 0 0 0 0 0 0 0

0 0 0 160 299 159 131 146 138 146 141 158 146 125 152 0 0 0 0 0 0 0

0 0 0 144 369 162 125 142 145 153 144 135 157 159 153 0 0 0 0 0 0 0

0 0 0 169 298 180 132 132 165 130 133 115 189 149 135 0 0 0 0 0 0 0

0 0 0 148 348 171 127 159 132 147 142 132 164 181 142 0 0 0 0 0 0 0

0 0 0 132 307 178 138 122 152 123 150 147 170 190 155 0 0 0 0 0 0 0

0 0 0 144 304 160 156 147 147 152 109 149 152 148 160 0 0 0 0 0 0 0

0 0 0 128 286 156 143 143 161 123 119 140 154 170 145 0 0 0 0 0 0 0

0 0 0 131 275 189 120 151 112 141 165 145 157 177 128 0 0 0 0 0 0 0

0 0 0 144 295 185 134 134 133 133 143 155 146 161 145 0 0 0 0 0 0 0

0 0 0 139 329 198 116 147 144 150 128 116 165 176 119 0 0 0 0 0 0 0

0 0 0 135 335 151 138 152 130 138 135 131 155 182 136 0 0 0 0 0 0 0

0 0 0 142 326 157 136 132 128 138 122 115 161 159 145 0 0 0 0 0 0 0

Table 7: Global horizontal irradiance per scenario I g , s (w/m2)

Time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

1

2

3

4

5

6

7

8

9

10

11

12

14

14

15

16

17

18

19

20

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

70

64

67

79

89

74

75

94

89

80

94

83

74

80

72

73

81

78

75

79

492

471

467

471

462

397

488

584

444

549

443

517

456

451

425

408

438

489

497

484

501

720

747

702

541

634

689

694

604

614

683

650

675

607

593

716

702

753

573

595

704

806

738

909

704

670

819

868

768

733

774

743

810

914

834

705

785

678

808

794

1282

1088

996

1125

891

972

1146

1139

1056

1030

960

1152

885

1062

1038

1097

974

1067

1098

954

1052

1250

1051

993

1070

1001

1111

1016

1037

1091

1238

992

1141

1105

1214

846

1000

1082

978

962

1137

1111

1102

1122

897

1035

1064

1001

1138

1191

1015

1143

960

1183

960

1101

1040

1170

1078

1074

1116

962

987

1179

828

1193

912

1043

1022

1045

964

1031

1088

793

862

1196

1039

927

976

884

835

832

851

799

855

786

996

773

1021

867

741

854

946

963

900

933

1001

748

844

740

633

733

733

773

707

591

791

751

653

700

842

732

761

681

687

703

650

739

693

718

503

472

527

511

572

571

553

471

423

538

502

612

640

500

575

597

543

593

614

537

245

235

186

228

239

232

223

266

253

255

223

236

257

265

241

212

240

197

225

241

19

Journal Pre-proof

18 19 20 21 22 23 24

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Table 8: Ambient temperature per scenario Tt ,as (0C)

Time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

1

2

3

4

5

6

7

8

9

10

11

12

14

14

15

16

17

18

19

20

19.9 19.1

22.6 24.1

21.5 23.5

22.8 23.8

21.9 23.3

22.0 22.0

20.4 21.9

21.0 24.5

17.9 21.4

25.7 24.5

23.4 24.3

25.9 24.9

20.3 22.5

25.7 23.3

24.4 26.2

22.9 22.2

22.2 19.0

21.0 25.0

24.0 23.3

20.8 21.7

28.9

20.9

23.6

23.3

22.0

20.2

18.2

22.2

20.6

24.0

21.9

24.9

24.1

23.1

20.6

26.6

21.2

25.9

20.9

21.9

19.6 22.3 20.6 26.0 19.9 22.7 34.6 28.0 27.4 31.1 26.0 24.4 25.2 27.6 28.0 27.1 23.1 27.3 23.4 25.6 22.8

23.5 20.9 18.8 24.9 28.5 26.0 29.4 33.3 26.8 26.8 25.9 28.2 23.6 26.5 26.5 25.7 24.6 24.8 22.3 23.7 25.3

20.6 24.5 19.9 24.7 29.6 23.8 26.9 28.0 26.6 27.5 26.5 28.2 26.3 20.9 24.2 26.9 26.1 22.8 22.9 21.5 25.0

18.8 27.5 23.4 24.9 27.8 29.4 30.4 26.5 27.1 32.9 24.8 29.8 25.6 25.7 26.0 22.6 24.7 25.7 23.3 23.2 23.1

24.0 18.3 26.2 24.4 21.4 22.7 24.1 28.5 21.7 23.1 26.6 27.2 28.6 27.0 23.8 25.1 18.5 20.8 19.9 23.1 24.7

21.8 22.8 21.9 21.0 25.1 21.7 26.2 26.7 25.0 33.3 24.4 22.7 28.5 26.1 29.0 25.0 24.4 19.8 26.2 27.8 27.3

23.6 19.5 22.2 25.8 27.3 26.5 30.9 29.6 25.7 25.4 31.0 30.5 27.7 25.2 29.8 21.2 23.0 20.2 19.8 24.2 25.3

22.0 24.5 27.6 30.9 27.5 28.0 30.7 27.1 24.2 29.1 24.0 28.9 23.6 30.0 27.0 23.4 23.0 21.1 23.0 24.7 24.8

23.4 27.7 26.3 23.5 23.9 24.8 28.5 27.6 27.5 28.5 31.7 25.2 21.1 28.5 23.6 22.6 20.6 22.3 25.5 24.9 20.6

18.1 19.2 23.7 29.0 24.3 23.7 27.8 29.1 28.8 29.2 27.0 27.0 26.9 28.7 24.1 25.4 25.4 22.2 22.7 22.6 22.8

25.7 26.1 27.8 23.4 27.1 25.0 25.9 33.0 24.5 26.9 23.0 32.4 25.1 25.2 22.7 22.6 22.3 18.1 24.0 23.6 24.0

24.6 17.8 24.4 27.3 25.8 24.0 31.1 26.4 27.6 28.8 26.5 28.2 30.6 26.6 26.2 27.0 21.7 23.6 25.5 23.8 23.3

24.2 23.6 21.7 24.1 26.7 26.2 23.9 30.4 23.2 30.4 29.4 29.3 32.0 29.0 27.2 26.3 22.4 20.3 26.1 21.1 19.6

24.7 24.3 23.7 23.8 24.0 29.5 28.7 29.4 28.6 22.1 29.9 26.2 25.0 29.9 27.6 23.3 22.6 20.9 26.8 23.9 21.8

22.0 22.7 21.1 22.5 23.5 27.0 28.0 32.3 23.2 24.1 28.0 26.5 28.7 27.1 24.7 24.0 23.6 24.2 21.3 24.7 25.8

23.3 25.3 21.5 21.6 28.4 22.8 29.6 22.5 26.6 33.4 29.0 27.1 29.8 23.9 24.9 25.2 23.7 25.9 21.8 23.1 18.4

23.1 25.4 23.8 23.1 27.8 25.4 26.3 26.7 25.1 29.0 31.1 25.0 27.2 27.0 21.8 26.3 22.7 28.0 26.3 25.8 26.1

22.8 23.3 22.9 25.8 29.8 21.9 28.8 28.8 28.3 25.8 23.2 28.5 29.7 22.2 27.4 24.7 22.7 23.8 23.9 24.9 20.2

21.3 20.1 22.2 26.3 22.7 26.1 29.6 26.1 26.0 27.2 26.2 26.7 30.7 25.4 24.0 24.5 23.4 29.8 23.4 22.7 24.5

21.1 20.8 23.3 25.6 23.6 25.7 25.8 25.6 25.9 24.6 23.0 27.7 26.8 27.1 22.3 22.9 24.3 23.7 24.0 23.2 23.5

It should be noted that the number of days for the studied horizon is 273. 3.2. Results In this section, simulations are carried out and the expected values of the result in different cases are presented. According to the obtained results, without taking RTP into account, the total expected operation cost of the RC in the defined horizon is $130.394, including the $866.490 cost of power imported from the upstream grid and the $736.096 revenue obtained from power exported to the upstream grid.

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In order to motivate energy consumers to revise their energy consumption pattern, the RTP of the DRP is employed. Thus, with considering this type of pricing, the total expected operation cost of the RC in the defined horizon is $81.733, including the $823.477 cost of power imported from the upstream grid and the $741.744 revenue obtained from power exported to the upstream grid. It is clear from the obtained results that by implementing the RTP of the DRP, the total expected cost of the RC is reduced up to 37.31%. In fact, by efficient charge and discharge processes of the EV system with RTP, economic goals of the RC are more satisfied, which appears to be suitable for the RC. For more comparison, numerical results without and with the RTP of the DRP are presented in Table 9. Also, total cost of RC including cost of purchasing power from upstream grid and revenue of selling power to the upstream grid is illustrated in Fig. 2. Table 9: Numerical optimization results (objective function) without and with RTP # Unit Value Without RTP With RTP Total expected cost $ 130.394 81.733 Import cost $ 866.490 823.477 Export revenue $ 736.096 741.744 Total cost reduction % 37.31

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1000 No RTP

900

With RTP

800

Value ($)

700 600 500 400 300 200 100 0 Total cost

Import cost

Export revenue

Fig. 2. Total cost of RC in detail without and with RTP

Non-critical demand with the RTP of DRP is shown in Fig. 3. According to this figure, the energy consumption pattern with RTP changes in a way to reduce the total payments of the RC. 4

No RTP

With RTP

Non-critical load (kW)

3.5 3 2.5 2 1.5 1 0.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time (hour) Fig. 3. Non-critical demand with RTP

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Total imported power from the upstream grid is shown in Fig. 4. Based on this figure, power imported from the upstream grid decreases with RTP; therefore, the total cost of the RC decreases.

Imported power from upstream grid (kW)

5

No RTP

With RTP

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time (hour)

Fig. 4. Power imported from the upstream grid

Moreover, as shown in Fig. 5, total exported power from the RC to the upstream grid increases with RTP, which leads to more benefits.

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Exported power to upstream grid (kW)

2.5

No RTP

With RTP

2

1.5

1

0.5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (hour)

Fig. 5. Power exported to the upstream grid

Charge and discharge rates of the EV without and with RTP are depicted in Figs. 6 and 7, respectively. As shown in these figures, the EV is optimally charged and discharged with RTP to balance the intermittent output of the PV system and supply energy demand.

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Fig. 6. The charge power of the EV

Fig. 7. The discharge power of the EV

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To illustrate the effect of the stochastic nature of the SOC at the arrival time of the EV, the total operation cost of RC without and with RTP is presented for all the scenarios in Table 10. Table 10: Total cost without and with RTP Without RTP Scenario Total Scenario Total cost ($) cost ($) 216.375 85.408 1 11 166.516 160.884 2 12 196.332 140.683 3 13 133.081 120.147 4 14 52.933 94.363 5 15 183.008 158.058 6 16 102.030 214.188 7 17 97.884 156.479 8 18 105.096 186.035 9 19 157.387 161.780 10 20

Scenario 1 2 3 4 5 6 7 8 9 10

With RTP Total Scenario cost ($) 167.416 11 117.512 12 137.122 13 88.736 14 11.571 15 130.270 16 101.643 17 47.950 18 58.434 19 101.174 20

Total cost ($) 38.856 107.531 88.452 69.802 45.613 111.007 166.465 104.769 138.203 109.911

It is clear from Table 10 that under the SOC value in different scenarios, the EV integrated into other energy units can present various kinds of performance, which can result in different economic performances. 4. Conclusion Different types of DG units can be integrated in RCs to supply energy demands with their local generation. RCs including energy units such as EV and PV units that are accurately modeled can exchange energy with upstream grids to gain benefits. In this paper, a mathematical-based optimization framework was presented for the optimal integration of a PV unit and an EV into a grid-connected RC, in which the employed energy units were modeled through precise mathematical-based models to make simulation results as precise as possible. Moreover, the RTP mechanism of demand response was implemented to enhance the system economic performance and the consumer’s behavior was analyzed toward the proposed prices within the mentioned mechanism. According to the simulation results, the proposed models for energy units in the RC were optimally configured and the optimal economic operation of the RC was obtained. Moreover, 26

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power generated by the PV unit was efficiently used to supply energy demand and charge the EV. Later, the stored energy was released to be either exported or used for supplying the demand. In addition, in accordance with power prices, within the periods with lower prices, the upstream grid power was imported to help the RC satisfy energy demands. It should be noted that different scenarios were generated to model stochastic driving patterns at the arrival time of the EV. It can be observed that the revenue obtained from exporting excess power generated by the PV unit can provide economic benefits for the RC. After applying RTP, the discussed economic results were enhanced since the total expected cost of the operating RC with RTP was reduced by 37.31%, which showed the optimal performance of energy units integrated into the RC with RTP. Energy units including PV systems and EVs can have more efficient performance with RTP, which could lead to a reduction in the total operation cost of the RC. It should be mentioned that the value of the obtained numerical results, such as cost-saving percentage, depends on the test system. The proposed mathematical model is easily applicable to other cases and can be extended to other systems with different energy mixes. Via extending the proposed model, one can study the probabilistic performance of the RC using different methodologies such as the chance-constraint method in future works. References Abedini, M., Moradi, M.H., Hosseinian, S.M., 2016. Optimal management of microgrids including renewable energy scources using GPSO-GM algorithm. Renew. Energy. https://doi.org/10.1016/j.renene.2016.01.014 Aghajani, G.R., Shayanfar, H.A., Shayeghi, H., 2017. Demand side management in a smart micro-grid in the presence of renewable generation and demand response. Energy. https://doi.org/10.1016/j.energy.2017.03.051

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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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

Optimal Scheduling of renewable-based residential complex.



Utilization of EV to handle intermittent generation of PV unit.



Implementation of RTP to reduce total operation cost of RC.